The Role of Calculi in Uncertain Reasoning

Abstract: Much of the controversy about methods for automated decision making has
focused on specific calculi for combining beliefs or propagating uncertainty.
We broaden the debate by (1) exploring the constellation of secondary tasks
surrounding any primary decision problem, and (2) identifying knowledge
engineering concerns that present additional representational tradeoffs. We
argue on pragmatic grounds that the attempt to support all of these tasks
within a single calculus is misguided. In the process, we note several
uncertain reasoning objectives that conflict with the Bayesian ideal of
complete specification of probabilities and utilities. In response, we
advocate treating the uncertainty calculus as an object language for reaoning
mechanisms that support the secondary tasks. Arguments against Bayesian
decision theory are weakened when the calculus is relegated to this role.
Architectures for uncertainty handling that take statements in the calculus as
objects to be reasoned about offer the prospect of retaining normative status
with respect to decision making while supporting the other tasks in uncertain
reasoning.